A stringed instrument having a body and a neck from the body with a fingerboard on that neck, the body being provided with a bridge for supporting first end portions of a plurality of strings, a nut with predetermined fixed loci for supporting second end portions of said plurality of strings being provided near an end of the fingerboard, away from the body, and that fingerboard being provided with a plurality of frets between said bridge and said nut, a first fret being defined as the fret closest to the nut, said loci having front portions located at a side of the nut facing said first fret and being designed to support a plurality of strings arranged in accordance with a series of decreasing thickness, each front portion of said loci having a predetermined fixed distance to said first fret.
Since quite some time, it is known that guitars in their most basic form, i.e., with frets, placed according to the well-known "1/18th rule", suffer from bad intonation. The 1/18-rule states that the ratio between the distance from one fret to the bridge and the distance from an adjacent fret to that bridge equals the twelfth root of 2. The bad intonation is mainly due to the elongating of the sting as a result of the longer path the string has to travel from bridge to nut when the string is pressed towards the fingerboard by a user's finger. The string no longer follows the shortest route, but goes from the bridge to the fingerboard, partially follows the shape of the finger and goes back up again to the nut.
For example, in U.S. Pat. No. 5,570,910 a method is disclosed to obtain better intonation. An adjustable bridge and an adjustable nut are used to compensate for the length changes of the strings. In this way, the intonation of the guitar can be controlled on two sides of the strings and a perfect intonation is accomplished. Guitars of today, however, are seldom equipped with both an adjustable nut and an adjustable bridge, as they are complex to build and thus expensive. Also, with both the bridge and the nut being adjustable, adjusting a guitar to a perfect intonation is not an easy task, since the position of the nut, the position of the bridge and the position of the frets are codependent. Adjusting the instrument to a perfect intonation becomes a process of trial and error, but a perfect intonation for all strings can be accomplished though. A further drawback of adjustable nuts is that they worsen the tone quality. This is mainly because they are made of separate parts and thus do not guide the vibrations from the strings to the guitar very well.
In U.S. Pat. No. 5,728,956 an alternative nut is disclosed that can be used in combination with an adjustable bridge. According to this publication, the elongation of the fretted strings is compensated by shortening the distance between the nut and the first fret by approximately 3.3%. It is claimed that this results in an accurate intonation on all fret positions.
The latter solution, however, does not take into account the uneven sensitivity for elongation of different string types. For example, thinner strings tend to cut into the flesh of the finger relatively more than thicker strings. Therefore, the thinner strings may be less flexed in the area where they are pressed down to the fingerboard than thicker strings are.
Since, apparently, a relation exists between the elongation of the string, whatever its source, and its physical properties and dimensions, the nut should be adapted for that to obtain a better intonation.